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A method for evaluating general performance indices for the time and frequency response for the free motion of a linear stationary discrete control system described by the matrix equation is given. A matrix B is formed from the system matrix A. The transpose of the inverse of the matrix B and its powers is then used to evaluate the expressions and where is a quadratic algebraic form, Δ m is the mth forward difference, and r = 0, 1, 2, …. From these expressions performance indices for the time and frequency response were then determined.

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For the control of a multi-input, multi-output process with time delays, algorithms for noninteractive control with time delay compensation are developed. These are then applied to a 3 input, 3 output process, to obtain the 3×3 noninteracting algorithms. To test and study the behavior of such a control system, simulation techniques are found to be very useful not only in designing and testing the control system but also in investigating and correcting for its limitations. Simulation results are presented and discussed. Although these algorithms are general and have been used in various industry applications, the major contribution of this paper is the application of the developed theory in the paper industry. For a fine paper machine, the major quality variables are basis weight, moisture and opacity. Control of these variables is effected by adjustment of stock flow, steam pressure and TiO2 flow. Mathematically this process includes time delay and dynamics in addition to cross-coupling effects. The control algorithms developed here are implemented using a digital process control computer. Field results are presented and discussed in detail.